What is the solution for y^{''}+4y^'+3y=6e^{-5t} ?

The solution for y^{''}+4y^'+3y=6e^{-5t} is y=c_{1}e^{-t}+c_{2}e^{-3t}+3/4 e^{-5t}

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y^{''}+4y^'+3y=6e^{-5t}

y^{^{''}} + 4 y^{^{'}} + 3 y = 6 e^{- 5 t}

y = c_{1} e^{- t} + c_{2} e^{- 3 t} + \frac{3}{4} e^{- 5 t}

Solution steps

y^{''} (t) + 4 y^{'} (t) + 3 y = 6 e^{- 5 t}

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} e^{- 3 t} + \frac{3}{4} e^{- 5 t}

y = c_{1} e^{- t} + c_{2} e^{- 3 t} + \frac{3}{4} e^{- 5 t}

What is the solution for y^{''}+4y^'+3y=6e^{-5t} ?
The solution for y^{''}+4y^'+3y=6e^{-5t} is y=c_{1}e^{-t}+c_{2}e^{-3t}+3/4 e^{-5t}